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A common approach to interpreting the quasi-elastic neutron scattering function, S(Q,ω), arising from diffusive processes is to use an analytic rate equation model. Such models, however, rely on simplifying assumptions and are usually defined in the mean-field limit. They are generally only applicable to low concentrations and where the interactions between the diffusing species can be neglected; higher concentrations and finite interactions (relative to kT) give rise to correlation effects which are difficult to account for analytically. The advantage of Monte Carlo simulation is that interactions and correlation effects are explicitly accounted for. We describe a method for the calculation of both the incoherent and coherent scattering functions from Monte Carlo simulation of particle diffusion. Results are presented for diffusion on an FCC lattice, showing how the broadening from incoherent scattering is reduced, at finite concentrations of the diffusing species, by particle correlation. The coherent broadening, however, is not a function of concentration, when there are no interactions. The effect of interactions on the form of the coherent broadening is also discussed. |
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